The publication of the sequence of the human genome and breakthroughs in the high throughput technologies for single nucleotide polymorphism (SNP) genotyping, gene expression, and protein measurements have offered new opportunities for the study of genome complexity. New technologies are generating large amounts of high dimensional data at an astounding speed. Relative to the high dimension of the data the number of independent samples is often rather small, either because the techniques are too expensive, or because it is hard to obtain enough independent biological samples. Clearly, the development of new statistical techniques is required for the extraction of useful biological information from such data. Adaptive regression methods, which combine variable selection and nonlinear modeling, are well suited for many of these problems. The aim of this proposal is to develop and enhance these methods to address the practical problems that arise directly from several collaborative projects. In particular we focus on association studies with SNP and microarray data. For SNP association studies we plan to make use of Logic Regression. This methodology combines mostly binary predictors using rules of Boolean algebra. The proposed developments include new techniques to deal with haplotype data, new approaches to model selection that scale up to high-dimensional problems, and computational techniques that make it feasible to deal with large data sets. For the analysis of microarray association studies we plan to use polynomial splines, an approach that combines nonlinear functions of predictors and low-order interactions. Gene expression measurements usually have a large variance, and measurements for different genes are often highly correlated. This, combined with the high dimensionality, makes regularization a necessity. Therefore, another focus of this proposal is to develop methods for combining predictors or models to regularize the model selection process. In addition, we plan to develop methods to improve inference for polynomial spline methodologies.